Look at the left triangle first. Opposite the 30 degree angle (not shown) is the shortest side, which (according to the sine function) is half the hypotenuse, or 2√3. Then (2√3)² + x² = (4√3)², or
4(3) + x² = 16(3). Thus, x² = 16(3) - 4(3) = 12(3) = 36, and so x = 6. Again using the sine function, we find that x = 2y = 6, so, using the sine function, we find that sin 30° = 6/y. Thus y = 6 / (2/1) = 12 = y
